per the question from a gamer-
“how is fatigue handled under these rules?”

The Brigade or Battery will pick up fatigue from movement, formation changes, firing, and melee. This is in the thought process of the Friction of battle, it could be looked at as physical – the men are tired, stragglers – men increasing falling out of ranks, equipment – gun barrels are fouled, cohesion of the unit – officers are losing control. This friction is measured in the game by the term Efficiency Points. These directly reduce the fighting strength of the Brigade/Battery. If the Brigade/Battery has the chance to reform for a turn, i.e. not in combat, the Brigadier can attempt to restore order, how much is not known.  An example would be during the Pickett/Pettigrew charge on July 3 at Gettysburg, as the rebels advanced they entered a swale about half way across the field, this allowed the unit to halt and officers to reform ranks, close ranks, collect straggers etc. from long range artillery fire, the officers cry “take a breath men”.
For the artillery crews, the act of firing the battery for a turn causes this lost as well, with the risk of ammo and the physical effect, it is not uncommon to see a battery rest for turn vs. the game where we just fire away.
Another example in a recent game, 1st day of the Seven Days at Oak Grove, Virginia; Gen. Sickles moves his brigade across White Oak Swamp, it is heavy rough, slows the unit down, Gen. Sickles is pushing to clear the wet land and reach the higher ground.  He orders the unit at the Double Time, the unit is hit hard by E-factors, he gets the ground but is in bad shape. The Rebels under Gen. Huger advance into a Skirmish fight which does not allow Sickles to reform, he now is in a bad spot.  During the next turn, with the brigade in trouble, it fails morale, falls back over the stream, and picks up more e’factors in the process. It will take time to reorder the unit, although it has very little strength point loses it is wrecked due to friction. With luck and good officers Gen. Sickles Brigade will recover and could re-enter the battle in an hour.